Solve for $x$ and $y$ using elimination. ${-3x-3y = -30}$ ${3x-2y = -10}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-5y = -40$ $\dfrac{-5y}{{-5}} = \dfrac{-40}{{-5}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-3y = -30}\thinspace$ to find $x$ ${-3x - 3}{(8)}{= -30}$ $-3x-24 = -30$ $-3x-24{+24} = -30{+24}$ $-3x = -6$ $\dfrac{-3x}{{-3}} = \dfrac{-6}{{-3}}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {3x-2y = -10}\thinspace$ and get the same answer for $x$ : ${3x - 2}{(8)}{= -10}$ ${x = 2}$